The sheaves parameterized by the fibers \(M_C\)  and \(N_C\)  can be divided into two types, namely sheaves of type I and type II (cf. [1]}). A sheaf \({F}\)  on \(J\)  with Fitting support \(C = 2C_{\textup {red}}\)  is said to be of type \(I\)  if the composition of the natural morphisms \(\mathcal {O}_J \rightarrow \mathcal {O}_C \rightarrow \mathcal {E}nd_J({F})\)  factors via the natural surjection \(\mathcal {O}_J \rightarrow \mathcal {O}_{C_{\textup {red}}}\)  and is said to be of type \(II\)  otherwise. In particular, sheaves of type \(I\)  are sheaves on \(J\)  with schematic support \(C_{\textup {red}}\)  and sheaves of type \(II\)  are sheaves on \(J\)  with schematic support \(C\) .
